A circle has a circumference of $16\pi$. It has an arc of length $12\pi$. What is the central angle of the arc, in degrees? ${16\pi}$ ${270^\circ}$ $\color{#DF0030}{12\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{s}{c}$ $\dfrac{\theta}{360 ^ \circ} = 12\pi \div 16\pi$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{3}{4}$ $\theta = \dfrac{3}{4} \times 360 ^ \circ$ $\theta = 270^\circ$